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Two blocks are connected to an ideal spr...

Two blocks are connected to an ideal spring of stiffness `200 N//m`. At a certain moment, the two block are moving in opposite diretion with speeds `4 ms_(1)` and ' 6 ms_(1) ' the instantaneous elongation of the spring `10 cm`, The rate at which the spring energy `(kx^(2)/(2))` is increasing is.

A

`500 J//s`

B

`400 J//s`

C

`200 J//s`

D

`100 J//s`.

Text Solution

Verified by Experts

The correct Answer is:
C
Increase in potential energy per unit `=`decrease in kinetic energy of both
`=-d/(dt)(1/2m_(1)v_(1)^(2) + 1/2 m_(2)v_(2)^(2))`
`=v_(1)(-m(dv_(1))/(dt)) + v_(2) (-m_(2)(dv_(2))/(dt))`
`=v_(1)(-m_(1)a_(1)) + v_(2) (-m_(2)a_(2))`
or `(dU)/(dt) =v_(1) (-F_(1)) + v_(2) (-F_(2))`
Here, `=F_(1)=-F_(2) =kx=200xx0.1 =20N`
Substituting in Eq. (i) we have,
`(dU)/(dt) =(4)(20) + (6)(20)`
`=200 J//s`.
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